(a) m = [tex]\frac{1}{2}[/tex]
calculate the slope (m) using the ' gradient formula '
m = [tex]\frac{(y_{2 - y_{1)} } }{(x_{2 - x _{1)} } }[/tex]
let (x₁, y₁) = (8, 9) and (x₂, y₂) = ( - 2, 4)
m = [tex]\frac{(4 - 9)}{(-2 - 8)}[/tex] = [tex]\frac{-5}{-10}[/tex] = [tex]\frac{1}{2}[/tex]
(b) y - 9 = [tex]\frac{1}{2}[/tex] (x - 8)
the equation of a line in ' point- slope form ' is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
choose any of the 2 given points for (a, b) → (8, 9)
y - 9 = [tex]\frac{1}{2}[/tex] (x - 8) → " point- slope form"
(c) y = [tex]\frac{1}{2}[/tex] x + 5
the equation of a line in ' slope-intercept form ' is
y = mc + c
where m is the slope and c the y-intercept
expand and simplify the point- slope equation
y - 9 = [tex]\frac{1}{2}[/tex] x - 4
y = [tex]\frac{1}{2}[/tex] x - 4 + 9
y = [tex]\frac{1}{2}[/tex] x + 5 → " slope- intercept form"
